Simulations of cosmic ray propagation

Abstract

We review numerical methods for simulations of cosmic ray (CR) propagation on galactic and larger scales. We present the development of algorithms designed for phenomenological and self-consistent models of CR propagation in kinetic description based on numerical solutions of the Fokker–Planck equation. The phenomenological models assume a stationary structure of the galactic interstellar medium and incorporate diffusion of particles in physical and momentum space together with advection, spallation, production of secondaries and various radiation mechanisms. The self-consistent propagation models of CRs include the dynamical coupling of the CR population to the thermal plasma. The CR transport equation is discretized and solved numerically together with the set of MHD equations in various approaches treating the CR population as a separate relativistic fluid within the two-fluid approach or as a spectrally resolved population of particles evolving in physical and momentum space. The relevant processes incorporated in self-consistent models include advection, diffusion and streaming propagation as well as adiabatic compression and several radiative loss mechanisms. We discuss, applications of the numerical models for the interpretation of CR data collected by various instruments. We present example models of astrophysical processes influencing galactic evolution such as galactic winds, the amplification of large-scale magnetic fields and instabilities of the interstellar medium.

Cosmic ray-driven galactic winds: transport modes of cosmic rays and Alfvén-wave dark regions

“…Magnetic fields are mainly mediating the dynamics and the transport of CRs. CR protons with GeV energies dominate the total energy budget of the CR population and interact with the magnetic field in the following way: (i) CRs propagate along the large-scale magnetic field because the CR gyroradius is small compared to typical astrophysical scales in galaxies and in the ISM (Zweibel 2013;Zweibel 2017;Hanasz et al 2021), (ii) CRs interact with magnetic fluctuations of the turbulent cascade through resonant and non-resonant interactions (Yan & Lazarian 2004Lazarian & Xu 2022), and (iii) CRs themselves can drive small-scale magnetic perturbations by means of plasma physical processes and then interact with those magnetic fluctuations later on (Kulsrud & Pearce 1969;Shalaby et al 2021Shalaby et al , 2022.…”

Cosmic-Ray Transport in Varying Galactic Environments

“…In most studies of ISM dynamics and thermodynamics, the CR kinetic scales are much smaller than the spatial scales of interest and CRs must be approximated as a fluid. The transport of the CR fluid is generally described in terms of advection along with the background thermal gas velocity and either streaming at the local Alfvén speed or diffusing (primarily along the magnetic field) relative to the gas, or a combination of these (see review by Hanasz et al 2021). As explained above, the dichotomy between streaming and diffusion comes from the distinction between the self-confinement versus the extrinsic turbulence picture for the formation of scattering waves.…”

Cosmic-ray diffusion and the multi-phase interstellar medium in a dwarf galaxy. I. Large-scale properties and $γ$-ray luminosities

“…The dynamical role of CRs was first recognized by Parker (1966) who noted that, in a vertically stratified ISM, the magnetic and CR pressures would inflate the thermal gas and excite a vertical oscillation of the gas layer, named the Parker instability. Recent studies show that the instability growth rate depends on CR transport (see section 6.4 of Hanasz et al 2021).…”

“…The main CR component, ∼GeV protons and alpha particles, exchange energy collisionlessly with the thermal gas, through the local magnetic field, kinetic scale waves, and gyro-resonant streaming instabilities (Kulsrud 2005). CRs scatter off magnetic fluctuations that they can excite via resonant streaming instability ("self-confinement") or that are induced by interstellar Alfvénic turbulence ("extrinsic confinement") driven by stellar activity and cascading down to the micro-parsec scale of CR gyroradii (see reviews by Zweibel (2017) and Hanasz et al (2021)). In the Milky Way, breaks in the observed CR spectra suggest a possible transition between self-confinement in the disc and extrinsic diffusion at larger heights (few kpc) above the disc (Blasi et al 2012;Evoli et al 2018), but γ-ray observations of the vertical CR-flux gradient do not support this scenario (Joubaud et al 2020).…”

“…Conversely, while theory suggests that CR transport parameters should dramatically vary across gas phases and with the ambient magnetization level, the ensemble of CR observations (local CR spectra, secondary-to-primary ratios, γ-ray and radio intensities) can be explained to first order by assuming uniform and isotropic CR diffusion across the entire Milky Way (see reviews by Grenier et al 2015;Hanasz et al 2021). The good linear relation that is observed between γ-ray fluxes and total gas column densities in many directions across the Galactic disc implies that variations in CR density are at best modest (a smooth radial gradient by a factor of order four across the Milky Way), and that they are largely decoupled from the gas density and from star-formation activity (e.g.…”